To tackle the problem, let's first analyze the inequality given and translate it into a graph.
1. Understand the inequality:
[tex]\[
y < \frac{3}{4}x + 2
\][/tex]
This inequality represents a region below the line \( y = \frac{3}{4}x + 2 \).
2. Graph the boundary line \( y = \frac{3}{4}x + 2 \):
- The slope-intercept form of the equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Here, the slope \( m \) is \( \frac{3}{4} \) and the y-intercept \( b \) is \( 2 \).
- To graph this line, start at the y-intercept (0, 2) on the y-axis.
- From (0, 2), use the slope \(\frac{3}{4}\):
- Move up 3 units (rise) and to the right 4 units (run), arriving at the point (4, 5).
- Plot these points and draw a straight line through them. This line will be dashed, as the inequality is strict (\(<\) instead of \(\leq\)), indicating that points on the line are not included in the solution set.
3. Shade the correct region:
- Since the inequality is \( y < \frac{3}{4}x + 2 \), the region to be shaded is below the line.
4. Identify the correct graph from the choices:
- Look for the graph that features:
- A dashed line representing \( y = \frac{3}{4}x + 2 \).
- Shading below this line.
Now, examining the answer choices provided, you should look for the one that matches these criteria. Given that I don't have the actual graphs in front of me, you need to compare the described criteria to the graph choices (A, B, C, D).
Upon comparing, the correct graph will:
- Have a dashed boundary line.
- Reflect the slope 3/4, intercepting the y-axis at 2.
- Shade the region below this line.
Select the answer choice (Graph A, B, C, or D) that matches this description.
